Abstract
We extend here the many-times formalism, formerly used mainly for particles moving in given classical fields, to interacting particles. In order to minimize the difficulties associated with an equal-time interaction, we limit ourselves to nonrelativistic quantum mechanics and a two-particle interaction, such as that corresponding to the Coulomb force between charged particles. We obtain a set of differential equations which are really not consistent, but they serve as a guide to a formulation in terms of integral equations that has the same perturbation expansion as the usual theory for the scattering of particles. The integral equation for two-particle amplitudes can be modified to give the correct theory for bound states, but this is not the case for more than two particles. We expect that this theory can be generalized to a formulation of relativistic quantum mechanics of interacting particles.
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References
Bethe, H. A. and Salpeter, E. E. (1951).Physical Review,84, 1232.
Bethe, H. A. and Salpeter, E. E. (1957).Handbuch der Physik, Vol. XXXV:Atoms I, p. 282 (Ed. S. Flügge). Springer-Verlag, Berlin.
Bloch, F. (1934).Physikalische Zeitschrift der Sowjetunion,5, 301.
Dirac, P. A. M. (1932).Proceedings of the Royal Society (London),136, 453.
Dirac, P. A. M., Fock, V. A. and Podolsky, B. (1932).Physikalische Zeitschrift der Sowjetunion,2, 1932.
Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G. (1954).Tables of Integral Transforms, Vol. 1. McGraw-Hill, New York.
Feynman, R. P. (1949).Physical Review,76, 749.
Fronsdal, C. (1971).Physical Review,D4, 1689.
Fronsdal, C. and Lundberg, L. E. (1970).Physical Review,D1, 3247.
Goldberg, I. and Marx, E. (1967).Nuclear Physics,B3, 25.
Goldberg, I. and Marx, E. (1968).Nuovo Cimento,57B, 485.
Marx, E. (1969).Nuoro Cimento,60A, 669.
Marx, E. (1970a).Nuovo Cimento,67A, 129.
Marx, E. (1970b).International Journal of Theoretical Physics, Vol. 3, No. 5, p. 401.
Marx, E. (1970c).International Journal of Theoretical Physics, Vol. 3, No. 6, p. 467.
Marx, E. (1972a).Nuovo Cimento,11B, 257.
Marx, E. (1972b).International Journal of Theoretical Physics, Vol. 5, No. 4, p. 251.
Marx, E. (1972c).International Journal of Theoretical Physics, Vol. 6, No. 5, p. 359.
Marx, E. (1972d).International Journal of Theoretical Physics, Vol. 6, No. 4, p. 307.
Rohrlich, F. (1965).Classical Charged Particles, p. 194. Addison-Wesley, Reading, Massachusetts.
Rzewuski, J. (1964).Field Theory, Part I:Classical Theory, pp. 124, 208. Polish Scientific Publishers, Warsaw.
Schwartz, L. (1954).Comptes Rendus,239, 847.
Schwinger, J. (1959).Physical Review Letters,3, 296.
Stueckelberg, E. C. G. (1941).Helvetica Physica Acta,14, 588.
Stueckelberg, E. C. G. (1942).Helvetica Physica Acta,15, 23.
Tomonaga, S. (1946).Progress in Theoretical Physics,1, 27.
Walter, J. F. and Marx, E. (1971).Nuovo Cimento,3B, 119.
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Marx, E. Many-times formalism and Coulomb interaction. Int J Theor Phys 9, 195–217 (1974). https://doi.org/10.1007/BF01807524
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DOI: https://doi.org/10.1007/BF01807524